X-ray standing wave at the total reflection condition

Fresnel theory is used to derive the complex electric fields above and below an X-ray reflecting interface that separates two materials with differing refraction indices. The interference between the incident and reflected waves produces an X-ray standing wave (XSW) above the reflecting interface. The XSW intensity modulation is strongly enhanced by the total external reflection condition, which occurs at incident angles less than the critical angle. At these small milliradian incident angles, the XSW period (?/2?) becomes very large, which makes the TR-XSW an ideal probe for studying low-density structures that extend 1 to 1000 nm above the reflecting interface.